Processing Math: Done

From Förberedande kurs i matematik 1

Let's write down the equation for a straight line as

y=kx+m

where k and m are constants which we shall determine.

Since the points (2,3) and (3,0) should lie on the line, they must also satisfy the equation of the line,

3=k2+mand0=k3+m.

If we take the difference between the equations, m disappears and we can work out the slope k,

3−03=k2+m−(k3+m)=−k.

Substituting this into the equation 0=k3+m then gives us a value for m,

m=−3k=−3(−3)=9.

The equation of the line is thus y=−3x+9.

Note. To be completely certain that we have calculated correctly, we check that the points (2,3) and (3,0) satisfy the equation of the line:

• (x,y) = (2,3): LHS=3  and  RHS=−32+9=3.
• (x,y) = (3,0): LHS=0  and  LHS=−33+9=0.